Abstract

A novel alternating-direction implicit method is developed for the full-vectorial wave equation. The cross-coupling terms are split off from the full-vectorial propagation operator, and their inversions are performed separately by a noniterative method at each step. The present method shows good performance in efficiency by comparison with the iterative method. It can be proved that the algorithm is of second-order accuracy along the propagating direction. To examine the accuracy of the present algorithm, it is compared with previously presented formulas, and the results show that it maintains high accuracy.

© 2007 Optical Society of America

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  1. W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
    [CrossRef]
  2. A. Behie and P. K. W. Vinsome, Soc. Pet. Eng. J. 22, 658 (1982).
  3. H. A. Van Der Dorst, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 13, 631 (1992).
  4. J. Yamauchi, G. Takahashi, and H. Nakano, J. Lightwave Technol. 16, 2458 (1998).
    [CrossRef]
  5. I. Mansour, A. D. Capobianco, and C. Rosa, J. Lightwave Technol. 14, 908 (1996).
    [CrossRef]
  6. S. L. Chui and Y. Y. Lu, J. Opt. Soc. Am. A 21, 420 (2004).
    [CrossRef]
  7. D. Yevick, W. Bardyszewski, and M. Glasner, IEEE Photon. Technol. Lett. 7, 658 (1995).
    [CrossRef]
  8. D. Yevick, IEEE Photon. Technol. Lett. 12, 1636 (2000).
    [CrossRef]
  9. A. Jennings, Matrix Computation for Engineers and Scientists (Wiley, 1977).
  10. D. Yevick and W. Bardyszewski, Opt. Lett. 17, 329 (1992).
    [CrossRef] [PubMed]
  11. C. L. Xu, W. P. Huang, and S. K. Chaudhuri, J. Lightwave Technol. 11, 1209 (1993).
    [CrossRef]
  12. S. Jügling and J. C. Chen, IEEE J. Quantum Electron. 30, 2098 (1994).
    [CrossRef]
  13. T. Ando, H. Nakayama, J. Yamauchi, and H. Nakano, J. Lightwave Technol. 20, 1627 (2002).
    [CrossRef]
  14. W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, IEEE Photon. Technol. Lett. 8, 649 (1996).
    [CrossRef]
  15. Y. Y. Lu and J. Zhu, IEEE Photon. Technol. Lett. 17, 2601 (2005).
    [CrossRef]
  16. H. Deng and D. Yevick, IEEE Photon. Technol. Lett. 17, 1429 (2005).
    [CrossRef]

2005

Y. Y. Lu and J. Zhu, IEEE Photon. Technol. Lett. 17, 2601 (2005).
[CrossRef]

H. Deng and D. Yevick, IEEE Photon. Technol. Lett. 17, 1429 (2005).
[CrossRef]

2004

2002

2000

D. Yevick, IEEE Photon. Technol. Lett. 12, 1636 (2000).
[CrossRef]

1998

1996

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, IEEE Photon. Technol. Lett. 8, 649 (1996).
[CrossRef]

I. Mansour, A. D. Capobianco, and C. Rosa, J. Lightwave Technol. 14, 908 (1996).
[CrossRef]

1995

D. Yevick, W. Bardyszewski, and M. Glasner, IEEE Photon. Technol. Lett. 7, 658 (1995).
[CrossRef]

1994

S. Jügling and J. C. Chen, IEEE J. Quantum Electron. 30, 2098 (1994).
[CrossRef]

1993

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

C. L. Xu, W. P. Huang, and S. K. Chaudhuri, J. Lightwave Technol. 11, 1209 (1993).
[CrossRef]

1992

H. A. Van Der Dorst, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 13, 631 (1992).

D. Yevick and W. Bardyszewski, Opt. Lett. 17, 329 (1992).
[CrossRef] [PubMed]

1982

A. Behie and P. K. W. Vinsome, Soc. Pet. Eng. J. 22, 658 (1982).

1977

A. Jennings, Matrix Computation for Engineers and Scientists (Wiley, 1977).

Ando, T.

Bardyszewski, W.

D. Yevick, W. Bardyszewski, and M. Glasner, IEEE Photon. Technol. Lett. 7, 658 (1995).
[CrossRef]

D. Yevick and W. Bardyszewski, Opt. Lett. 17, 329 (1992).
[CrossRef] [PubMed]

Behie, A.

A. Behie and P. K. W. Vinsome, Soc. Pet. Eng. J. 22, 658 (1982).

Capobianco, A. D.

I. Mansour, A. D. Capobianco, and C. Rosa, J. Lightwave Technol. 14, 908 (1996).
[CrossRef]

Chaudhuri, S. K.

C. L. Xu, W. P. Huang, and S. K. Chaudhuri, J. Lightwave Technol. 11, 1209 (1993).
[CrossRef]

Chen, J. C.

S. Jügling and J. C. Chen, IEEE J. Quantum Electron. 30, 2098 (1994).
[CrossRef]

Chui, S. L.

Deng, H.

H. Deng and D. Yevick, IEEE Photon. Technol. Lett. 17, 1429 (2005).
[CrossRef]

Glasner, M.

D. Yevick, W. Bardyszewski, and M. Glasner, IEEE Photon. Technol. Lett. 7, 658 (1995).
[CrossRef]

Huang, W. P.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, IEEE Photon. Technol. Lett. 8, 649 (1996).
[CrossRef]

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

C. L. Xu, W. P. Huang, and S. K. Chaudhuri, J. Lightwave Technol. 11, 1209 (1993).
[CrossRef]

Jennings, A.

A. Jennings, Matrix Computation for Engineers and Scientists (Wiley, 1977).

Jügling, S.

S. Jügling and J. C. Chen, IEEE J. Quantum Electron. 30, 2098 (1994).
[CrossRef]

Lu, Y. Y.

Y. Y. Lu and J. Zhu, IEEE Photon. Technol. Lett. 17, 2601 (2005).
[CrossRef]

S. L. Chui and Y. Y. Lu, J. Opt. Soc. Am. A 21, 420 (2004).
[CrossRef]

Lui, W.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, IEEE Photon. Technol. Lett. 8, 649 (1996).
[CrossRef]

Mansour, I.

I. Mansour, A. D. Capobianco, and C. Rosa, J. Lightwave Technol. 14, 908 (1996).
[CrossRef]

Nakano, H.

Nakayama, H.

Rosa, C.

I. Mansour, A. D. Capobianco, and C. Rosa, J. Lightwave Technol. 14, 908 (1996).
[CrossRef]

Takahashi, G.

Van Der Dorst, H. A.

H. A. Van Der Dorst, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 13, 631 (1992).

Vinsome, P. K. W.

A. Behie and P. K. W. Vinsome, Soc. Pet. Eng. J. 22, 658 (1982).

Xu, C. L.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, IEEE Photon. Technol. Lett. 8, 649 (1996).
[CrossRef]

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

C. L. Xu, W. P. Huang, and S. K. Chaudhuri, J. Lightwave Technol. 11, 1209 (1993).
[CrossRef]

Yamauchi, J.

Yevick, D.

H. Deng and D. Yevick, IEEE Photon. Technol. Lett. 17, 1429 (2005).
[CrossRef]

D. Yevick, IEEE Photon. Technol. Lett. 12, 1636 (2000).
[CrossRef]

D. Yevick, W. Bardyszewski, and M. Glasner, IEEE Photon. Technol. Lett. 7, 658 (1995).
[CrossRef]

D. Yevick and W. Bardyszewski, Opt. Lett. 17, 329 (1992).
[CrossRef] [PubMed]

Yokoyama, K.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, IEEE Photon. Technol. Lett. 8, 649 (1996).
[CrossRef]

Zhu, J.

Y. Y. Lu and J. Zhu, IEEE Photon. Technol. Lett. 17, 2601 (2005).
[CrossRef]

IEEE J. Quantum Electron.

W. P. Huang and C. L. Xu, IEEE J. Quantum Electron. 29, 2639 (1993).
[CrossRef]

S. Jügling and J. C. Chen, IEEE J. Quantum Electron. 30, 2098 (1994).
[CrossRef]

IEEE Photon. Technol. Lett.

W. P. Huang, C. L. Xu, W. Lui, and K. Yokoyama, IEEE Photon. Technol. Lett. 8, 649 (1996).
[CrossRef]

Y. Y. Lu and J. Zhu, IEEE Photon. Technol. Lett. 17, 2601 (2005).
[CrossRef]

H. Deng and D. Yevick, IEEE Photon. Technol. Lett. 17, 1429 (2005).
[CrossRef]

D. Yevick, W. Bardyszewski, and M. Glasner, IEEE Photon. Technol. Lett. 7, 658 (1995).
[CrossRef]

D. Yevick, IEEE Photon. Technol. Lett. 12, 1636 (2000).
[CrossRef]

J. Lightwave Technol.

I. Mansour, A. D. Capobianco, and C. Rosa, J. Lightwave Technol. 14, 908 (1996).
[CrossRef]

C. L. Xu, W. P. Huang, and S. K. Chaudhuri, J. Lightwave Technol. 11, 1209 (1993).
[CrossRef]

J. Yamauchi, G. Takahashi, and H. Nakano, J. Lightwave Technol. 16, 2458 (1998).
[CrossRef]

T. Ando, H. Nakayama, J. Yamauchi, and H. Nakano, J. Lightwave Technol. 20, 1627 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput.

H. A. Van Der Dorst, SIAM (Soc. Ind. Appl. Math.) J. Sci. Stat. Comput. 13, 631 (1992).

Soc. Pet. Eng. J.

A. Behie and P. K. W. Vinsome, Soc. Pet. Eng. J. 22, 658 (1982).

Other

A. Jennings, Matrix Computation for Engineers and Scientists (Wiley, 1977).

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Figures (2)

Fig. 1
Fig. 1

Evaluations of the efficiency in terms of (a) computational time per step versus the transverse mesh size and (b) comparison of memory between the present scheme and the iterative method.

Fig. 2
Fig. 2

R.E. of propagation constants of fundamental mode in ridge waveguide.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

ψ z = ( j 2 n 0 k 0 ) [ P ] ψ ,
P = M x x + M y y + M x y + M y x = [ P 11 x 0 0 P 22 x ] + [ P 11 y 0 0 P 22 y ] + [ 0 P 12 0 0 ] + [ 0 0 P 21 0 ] ,
P 11 x = x ( 1 n 2 ( n 2 ) x ) + ( n 2 n 0 2 ) 2 k 0 2 , P 22 x = 2 x 2 + ( n 2 n 0 2 ) 2 k 0 2 ,
P 22 y = y ( 1 n 2 ( n 2 ) y ) + ( n 2 n 0 2 ) 2 k 0 2 , P 11 y = 2 y 2 + ( n 2 n 0 2 ) 2 k 0 2 ,
P 12 = x ( 1 n 2 n 2 y ) 2 x y , P 21 = y ( 1 n 2 n 2 x ) 2 y x ,
[ 1 + j Δ z 4 n 0 k 0 ( M x x + M y y + M x y + M y x ) + ( j Δ z 4 n 0 k 0 ) 2 O ( M i j 2 ) + ( j Δ z 4 n 0 k 0 ) 3 O ( M i j 3 ) + ( j Δ z 4 n 0 k 0 ) 4 O ( M i j 4 ) ] ψ n + 1 = [ 1 j Δ z 4 n 0 k 0 ( M x x + M y y + M x y + M y x ) + ( j Δ z 4 n 0 k 0 ) 2 O ( M i j 2 ) ( j Δ z 4 n 0 k 0 ) 3 O ( M i j 3 ) + ( j Δ z 4 n 0 k 0 ) 4 O ( M i j 4 ) ] ψ n .
i = x y j = x y ( 1 + j Δ z 4 n 0 k 0 M i , j ) ψ n + 1 = i = x y j = x y ( 1 j Δ z 4 n 0 k 0 M i , j ) ψ n .
( 1 + j Δ z 4 n 0 k 0 M x x ) ψ n + 1 4 = ( 1 j Δ z 4 n 0 k 0 M y y ) ψ n ,
( 1 + j Δ z 4 n 0 k 0 M y y ) ψ n + 1 2 = ( 1 j Δ z 4 n 0 k 0 M x x ) ψ n + 1 4 ,
( 1 + j Δ z 4 n 0 k 0 M x y ) ψ n + 3 4 = ( 1 j Δ z 4 n 0 k 0 M y x ) ψ n + 1 2 ,
( 1 + j Δ z 4 n 0 k 0 M y x ) ψ n + 1 = ( 1 j Δ z 4 n 0 k 0 M x y ) ψ n + 3 4 .
P x y ψ = 1 4 Δ x Δ y [ ( n i 1 , j + 1 2 n i 1 , j 2 1 ) ψ i 1 , j + 1 + ( n i + 1 , j + 1 2 n i + 1 , j 2 1 ) ψ i + 1 , j + 1 + ( n i 1 , j 1 2 n i 1 , j 2 1 ) ψ i 1 , j 1 ( n i + 1 , j 1 2 n i + 1 , j 2 1 ) ψ i + 1 , j 1 ] ,

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